Sweeping Preconditioners for the Iterative Solution of Quasiperiodic Helmholtz Transmission Problems in Layered Media

David P. Nicholls, Carlos Pérez-Arancibia, Catalin Turc

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

Abstract

We present a sweeping preconditioner for quasi-optimal domain decomposition methods (DD) applied to Helmholtz transmission problems in periodic layered media. Quasi-optimal DD (QO DD) for Helmholtz equations rely on transmission operators that are approximations of Dirichlet-to-Neumann (DtN) operators. Employing shape perturbation series, we construct approximations of DtN operators corresponding to periodic domains, which we then use as transmission operators in a non-overlapping DD framework. The Robin-to-Robin (RtR) operators that are the building blocks of DD are expressed via robust boundary integral equation formulations. We use Nyström discretizations of quasiperiodic boundary integral operators to construct high-order approximations of RtR. Based on the premise that the quasi-optimal transmission operators should act like perfect transparent boundary conditions, we construct an approximate LU factorization of the tridiagonal QO Schwarz iteration matrix associated with periodic layered media, which is then used as a double sweep preconditioner. We present a variety of numerical results that showcase the effectiveness of the sweeping preconditioners applied to QO DD for the iterative solution of Helmholtz transmission problems in periodic layered media.

Original languageEnglish (US)
Article number44
JournalJournal of Scientific Computing
Volume82
Issue number2
DOIs
StatePublished - Feb 1 2020

All Science Journal Classification (ASJC) codes

  • Software
  • Theoretical Computer Science
  • Numerical Analysis
  • Engineering(all)
  • Computational Theory and Mathematics
  • Computational Mathematics
  • Applied Mathematics

Keywords

  • Domain decomposition methods
  • Helmholtz transmission problems
  • Periodic layered media
  • Sweeping preconditioners

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